Non-isothermal droplet spreading/dewetting and its reversal

Abstract

Axisymmetric non-isothermal spreading/dewetting of droplets on a substrate is studied, wherein the surface tension is a function of temperature, resulting in Marangoni stresses. A lubrication theory is first extended to determine the drop shape for spreading/dewetting limited by slip. It is demonstrated that an apparent angle inferred from a fitted spherical cap shape does not relate to the contact-line speed as it would under isothermal conditions. Also, a power law for the thermocapillary spreading rate versus time is derived. Results obtained with direct numerical simulations (DNS), using a slip length down to O(10 −4 ) times the drop diameter, confirm predictions from lubrication theory. The DNS results further show that the behaviour predicted by the lubrication theory -that a cold wall promotes spreading, and a hot wall promotes dewetting -is reversed at sufficiently large contact angles and/or viscosity of the surrounding fluid. This behaviour is summarized in a phase diagram, and a simple model that supports this finding is presented. Although the key results are found to be robust when accounting for heat conduction in the substrate, a critical thickness of the substrate is identified above which wall conduction significantly modifies wetting behaviour.

Rheology dictated spreading regimes of a non-isothermal sessile drop

“…This phenomenon is known as the thermocapillary or thermal Marangoni actuation of droplets (Young, Goldstein & Block 1959;Subramanian & Balasubramaniam 2001). The complex interfacial dynamics of droplet spreading over non-isothermal substrates have prompted a number of experimental and theoretical investigations over the last few decades (Ehrhard & Davis 1991;Brzoska, Brochard-Wyart & Rondelez 1993;Pratap, Moumen & Subramanian 2008;Gomba & Homsy 2010;Sui 2014;Chaudhury & Chakraborty 2015;Sui & Spelt 2015;Mac Intyre et al 2018;Dominguez Torres et al 2020;Xu et al 2021). The theoretical study of Ehrhard & Davis (1991) employed the lubrication approximation of the Navier-Stokes equations by exploiting the disparity between the length scale of the droplet along the spreading direction and the drop height.…”